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Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is…
Stochastic gradient descent is one of the most successful approaches for solving large-scale problems, especially in machine learning and statistics. At each iteration, it employs an unbiased estimator of the full gradient computed from one…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
In this paper, we propose a machine learning approach for forecasting hierarchical time series. When dealing with hierarchical time series, apart from generating accurate forecasts, one needs to select a suitable method for producing…
Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…
We propose a robust and computationally efficient algorithm to generically construct first return maps of dynamical systems from time series without the need for embedding. Typically, a first return map is constructed using a heuristic…
The forward estimation problem for stationary and ergodic time series $\{X_n\}_{n=0}^{\infty}$ taking values from a finite alphabet ${\cal X}$ is to estimate the probability that $X_{n+1}=x$ based on the observations $X_i$, $0\le i\le n$…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…
In a previous paper we have presented a CEGAR approach for the verification of parameterized systems with an arbitrary number of processes organized in an array or a ring. The technique is based on the iterative computation of parameterized…
A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…
We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…
Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…
We consider the problem of sequential evaluation, in which an evaluator observes candidates in a sequence and assigns scores to these candidates in an online, irrevocable fashion. Motivated by the psychology literature that has studied…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Previous preliminary results on the application of knowledge networks to noise reduction in stationary harmonic and weakly chaotic signals are extended to more general cases. The formalism gives a novel algorithm from which statistical…
Training Data Attribution (TDA) seeks to trace model predictions back to influential training examples, enhancing interpretability and safety. We formulate TDA as a Bayesian information-theoretic problem: subsets are scored by the…
Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…